\newproblem{lay:5_4_1}{
  % Problem identification
	\begin{large}
	  \hspace{\fill}\newline
    \textbf{Lay, 5.4.1}
	\end{large}
	\\
  \ifthenelse{\boolean{identifyAuthor}}{\textit{Carlos Oscar Sorzano, Aug. 31st, 2013} \\}{}

  % Problem statement
	Let $\mathcal{B}=\{\mathbf{b}_1,\mathbf{b}_2,\mathbf{b}_3\}$ and $\mathcal{D}=\{\mathbf{d}_1,\mathbf{d}_2\}$ be bases for vector spaces $V$ and $W$, respectively.
	Let $T:V\rightarrow W$ be a linear transformation with the property that
	\begin{center}
		$\begin{array}{l}
			T(\mathbf{b}_1)=3\mathbf{d}_1-5\mathbf{d}_2\\
			T(\mathbf{b}_2)=-\mathbf{d}_1+6\mathbf{d}_2\\
			T(\mathbf{b}_3)=4\mathbf{d}_2\\
		\end{array}$
	\end{center}
	Find the matrix of $T$ relative to $\mathcal{B}$ and $\mathcal{D}$
}{
  % Solution
	The matrix sought is
	\begin{center}
		$M=\begin{pmatrix} [T(\mathbf{b}_1)]_{\mathcal{D}} & [T(\mathbf{b}_2)]_{\mathcal{D}} & [T(\mathbf{b}_3)]_{\mathcal{D}} \end{pmatrix}=
		   \begin{pmatrix} 3 & -1 & 0\\-5&6&4\end{pmatrix}$
	\end{center}
	We can apply it as
	\begin{center}
		$[T(\mathbf{x})]_{\mathcal{D}}=M[\mathbf{x}]_{\mathcal{B}}$
	\end{center}
	
}
\useproblem{lay:5_4_1}
\ifthenelse{\boolean{eachProblemInOnePage}}{\newpage}{}
